Questions: Graph the given functions, (f) and (g), in the same rectangular coordinate system. Describe how the graph of (g) is related to the graph of (f). (f(x)=x) (g(x)=x-10) Use the graphing tool to graph the functions. How is the graph of (g) related to the graph of (f)? A. The graph of (g) is the graph of (f) shifted 10 units vertically up. B. The graph of (g) is the graph of (f) shifted 10 units vertically down. C. The graph of (g) is the graph of (f) shifted 10 units horizontally left. D. The graph of (g) is the graph of (f) shifted 10 units horizontally right.

Solution Steps

To graph the function $f(x) = p(x)$, plot the points of $p(x)$ on a rectangular coordinate system. This forms the graph of $f$ based on the given polynomial or function expression $p(x)$.

To graph $g(x) = p(x) + q$, take every point on the graph of $f(x)$ and shift it vertically by $q$ units. If $q > 0$, the shift is upwards; if $q < 0$, the shift is downwards. This results in a new graph that is identical in shape to $f(x)$ but is shifted vertically.

The graph of $g(x) = p(x) + q$ is the graph of $f(x)$ shifted downwards by $10$ units. This vertical shift is due to the addition of the constant $q$ to $p(x)$, which does not alter the shape of the graph but only its position relative to the y-axis.

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